﻿40 Dr. Dorothy Wrinch on the 



Our second approximation is therefore, 



■2X + 3/JL 



XH-3, 



X + /JL 



' 2 r2\4-3/x 2 /2\+jV 2 2 \ 



24\ A, + ^ }]' 



Any higher degree of approximation can also be obtained. 

 Our results stand in the form, 



and, in general, the form will be 



y s lr = d r 's + ia s r 2 . . . + s a s r 2s .... (2) 

 We easily see that if (2) be the form for ij s /r, then ' 



and the condition of zero radial traction, requiring that 



(X + 2/a) drig+ijdr + \r) s+1 /r = 

 on r=a, yields 



a g 2X + 3/A 9 2«« 3\4 5/x, 4 



uas+1 ~ 2 74TT7 a , + 176 ~Y+JT a ' * • 



6 .a s (s + l)\+(2s+l)fi 2s 



+ 2s-f-2.2s + 4 X + ^ 



so that 



W-2.4V ^ + y" J -4.-6V X + A* / 



+ 2s + 2.2s + 4V \+> / W 



When we have obtained a solution, 



p-r = q Vl + q2 V2 .. . +^ SJ 

 it is therefore possible to obtain a solution to a higher degree 



